Forming metal and other ductile materials into complex curved shapes with conventional methods is an expensive process. For example, forming curved shapes such as a hemispherical cap for a cylindrical, pressurized rocket fuel tank can be achieved by various conventional but expensive techniques. One such technique is spin forming in which material is placed over a mandrel, and the material and the mandrel are spun together on a lathe at high speeds. An external, local force can be applied to the material to form the material to the mandrel. Another technique is stretch forming in which a sheet of material is held at its edges and the center is pressed against a die to cause the sheet to take the shape of the die. Explosive forming is another conventional method that uses sudden, explosive pressure to cause a sheet of material to form to a die. Dish forming and head flanging operations are other methods used to form a cap or dome. While shapes such as a hemispherical shape may be produced in these ways, these techniques are difficult to perform, expensive, or yield inconsistent results.
FIGS. 1A and 1B show a conventional rolling technique involving three rollers 10, 11, and 12 used to form a material sheet 13 into a cylinder or partial cylinder. FIGS. 2A and 2B show a dish forming operation and a head flanging operation, respectively. The techniques shown in FIGS. 2A and 2B can be used to create compound curved shapes using a press 14 and a support 15. A material sheet 13 is held between the press 14 and the support 15. The shapes of the press 14 and support 15 give the sheet 13 a curved shape. A head flanging operation includes placing a material sheet 13 between a wheel 16 and die 17 to provide a sharper radius of curvature at the perimeter 18 of the sheet 13. FIG. 3 illustrates a system and technique for manufacturing semi-cylindrical sections using contoured roller pairs, each with a convex roller 20 and a concave roller 21. A material sheet 13 passes linearly through the rollers 20 and 21 to give the sheet 22 a U-shaped cross section. None of these techniques consistently produces compound curved sections (e.g., spherical sections) quickly and inexpensively.